Hi,

Is it possible to compute the elastic energy for a simple 2D cube before we 
solve the system?
Because I checked the displacement gradients and they are 0 due to having 
no solution probably.

Hence, I wonder how would someone be able to compute the elastic energy 
with the following formula:

psi = 0.5 * lambda * tr_eps * tr_eps + mu * tr_eps_2;

with 

tr_eps = trace(eps);
tr_eps_2 = trace(eps * eps);

Here eps is the strain tensor and lambda as well as mu are the lamé 
parameters, respectively.

In order to compute the strain tensor eps I need the displacement gradients:

 eps = 0.5 * (grad_u + transpose(grad_u));

And from what I checked, the get_strain() function from step-18 doesn't 
give me the same strain tensor. It seems more like a B-operator to me.

If I compute the elastic energy after I solved the system, how am I able to 
store the energy values for each cell, so I can have access to it all the 
time. 

>From Timo Heister and Thomas Wick's phase-field crack examples I learned 
that they compute energy by means of the compute_energy() function, but it 
seems to me like they just output the value and it is not further used 
during computation.

Kind regards,
S. A. Mohseni 

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